How To Make Volumetrics Round?
You could just consider the box to be a vector space in which you can sculpt your flame, by making its [ density | emission strength | color ] a function of the box's X,Y and Z.
Keeping it simple, here .. This box measures 2x2x4 Blender Units with its origin in the center of its base, and X,Y, and Z are measured in Object space.


(Left) By setting the density to 1 - the XYZ length, you get a hemisphere:



(Center) You could scale the Z to get an ellipsoid:



(Right) You could split the Z off as a multiplier, and sculpt it with a curve:


Of course you could extend this principle to vary colors, get flames-within-flames, etc. etc.